RIP Benoît Mandelbrot

October 20, 2010

It has already made the internet rounds, but it seems appropriate, given his popular appeal, to remark on the passing of mathematician Benoît Mandelbrot. Mandelbrot, perhaps best well known for coining the term fractal (and for his related popular work on the subject), died last week at the age of 85.

Mandelbrot's popularization of fractal geometry garnered him quite a bit of attention beginning in the 1980's. There is even a fractal named after him, the so-called "Mandelbrot set," which, like many fractals, is simple to generate, but looks complicated.

It's no coincidence that popularity in fractals rose in step with advancing computer technology. Without computers to perform the tedious calculations necessary for fractal generation (and by extension, to output all the pretty pictures), the field received much less attention. Contrary to popular belief, though, Mandelbrot was not the first to consider these ideas - indeed, many properties of fractal sets called "Julia sets" were first investigated by Pierre Fatou in the early twentieth century (as well as being further investigated by Gaston Julia, the man after whom the sets are now named). In fact, Scientific American ran an article last year which essentially asked how much of the mathematical credit Mandelbrot deserved. Such sentiments were also echoed in last week's New York Times obituary:

Dr. Mandelbrot received more than 15 honorary doctorates and served on the board of many scientific journals, as well as the Mandelbrot Foundation for Fractals. Instead of rigorously proving his insights in each field, he said he preferred to “stimulate the field by making bold and crazy conjectures” — and then move on before his claims had been verified. This habit earned him some skepticism in mathematical circles.

“He doesn’t spend months or years proving what he has observed,” said Heinz-Otto Peitgen, a professor of mathematics and biomedical sciences at the University of Bremen. And for that, he said, Dr. Mandelbrot “has received quite a bit of criticism.”

While his contributions from a rigorous mathematical standpoint may be up for debate, his influence in the realm of popular culture certainly isn't. His 1982 book The Fractal Geometry of Naturehighlighted the ubiquity of fractal patterns in nature, from small snowflakes to distant galaxies. Moreover, it was not written at a particularly technical level, and as a result, found a relatively large audience (especially for a book about contemporary mathematical research).

Of course, fractals and chaos became the hot topic during the latter half of the twentieth century, no doubt due in some part to Mandelbrot's influence. Without him, who knows whether or not we would have ever had the pleasure of witnessing Jeff Goldblum's performance of "chaoticiain" Ian Malcolm in not one, but two Jurassic Park films? While the term "chaos" as applied to mathematics has certainly lost some of its luster, I doubt that Mandelbrot's mathematical contributions (or at the very least, popularization of mathematical contributions) will soon be forgotten. Especially with songs like this!

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